Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In an arithmetic sequence, the first term,
a_(1), is equal to 5 , and the sixth term,
a_(6), is equal to 30 . Which number represents the common difference of the arithmetic sequence?

d=4

d=5

d=6

d=7

In an arithmetic sequence, the first term, $a_{1}$ , is equal to $5$ , and the sixth term, $a_{6}$ , is equal to $30$ . Which number represents the common difference of the arithmetic sequence? $\newline$ $d=4$ $\newline$ $d=5$ $\newline$ $d=6$ $\newline$ $d=7$

View step-by-step help

View step-by-step help

Convert a recursive formula to an explicit formula

Full solution

Q. In an arithmetic sequence, the first term,

a_{1}

, is equal to

5

, and the sixth term,

a_{6}

, is equal to

30

. Which number represents the common difference of the arithmetic sequence?

\newline

d=4

\newline

d=5

\newline

d=6

\newline

d=7

Given terms: We are given the first term of an arithmetic sequence, $a_{1} = 5$ , and the sixth term, $a_{6} = 30$ . We need to find the common difference, $d$ , of the sequence.
Arithmetic sequence formula: The $n$ th term of an arithmetic sequence can be found using the formula $a_n = a_1 + (n - 1)d$ , where $a_1$ is the first term and $d$ is the common difference.
Express sixth term: We can use the formula to express the sixth term: $a_{6} = a_{1} + (6 - 1)d = a_{1} + 5d$ .
Substitute values: Substitute the given values into the equation: $30 = 5 + 5d$ .
Solve for d: Solve for d: $30 = 5 + 5d$ implies $30 - 5 = 5d$ , so $25 = 5d$ .
Final common difference: Divide both sides by $5$ to find $d$ : $d = \frac{25}{5}$ , which gives us $d = 5$ .

More problems from Convert a recursive formula to an explicit formula

Question

Find the sum of the finite arithmetic series.

\sum_{n=1}^{10} (7n+4)

\newline

Posted 2 months ago

Question

Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`

Posted 1 month ago

Question

Type the missing number in this sequence: `2, 4 8`, ______,`32`

Posted 2 months ago

Question

What kind of sequence is this?

2, 10, 50, 250, \ldots

Choices:Choices:

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 2 months ago

Question

What is the missing number in this pattern?

1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_

Posted 1 month ago

Question

Classify the series.

\sum_{n = 0}^{12} (n + 2)^3

\newline

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 1 month ago

Question

Find the first three partial sums of the series.

\newline

1 + 6 + 11 + 16 + 21 + 26 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 1 month ago

Question

Find the third partial sum of the series.

\newline

3 + 9 + 15 + 21 + 27 + 33 + \cdots

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

S_3 =

Posted 1 month ago

Question

Find the first three partial sums of the series.

\newline

1 + 7 + 13 + 19 + 25 + 31 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 2 months ago

Question

Does the infinite geometric series converge or diverge?

\newline

1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots

\newline

\newline

\text{[A]converge}

\newline

\text{[B]diverge}

Posted 1 month ago